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In this paper, we present an electronic readout system for wireless passive sensors based on inductively coupled LC resonant circuits. The proposed system consists of a reader coil inductively coupled to the sensor circuit, an analog frontend circuit, and a digital signal processing unit. The analog frontend circuit generates a dc voltage representing the sensor resonance curve. The frequency of the reader coil driving signal is continuously readjusted by the digital signal processing unit. Based on analytical calculation and system simulation, we derive a model for the achievable accuracy of the overall sensor and readout system. The accuracy is limited by noise and systematic errors due to the measurement principle. We show how to design the digital signal processing system for optimal insensitivity to voltage noise. The noise sensitivity of the measurement system is inversely proportional to the square of the quality factor of the LC sensor. This means that minimizing the losses of the sensor is of crucial importance to obtain a wireless measurement system with a high range and a good insensitivity to noise. Subsequently, we outline an approach to calculate the sensor resonance frequency, quality factor, and inductive coupling factor from the available voltage signals in the signal processing unit using linear fitting functions. The accuracy of our approach is exemplified by a system simulation for typical sensor parameters. For the system studied, we show that the relative linearization error of the sensor resonance frequency measurement is below 0.02%. Taking the general models presented for both the noise sensitivity and linearization error into account, it is possible to estimate the maximum distance and accuracy for any wireless sensor system based on an inductively coupled LC resonator.